Question: Find an explicit formula for the arithmetic sequence $10,-10,-30,-50,...$. Note: the first term should be $\textit{c(1)}$. $c(n)=$
Answer: The general explicit formula for arithmetic sequences is ${a_1}+{d}(n-1)$, where ${a_1}$ is the first term and $ d$ is the common difference. The first term is ${10}$ and the common difference is ${-20}$. ${-20\,\curvearrowright}$ ${-20\,\curvearrowright}$ ${-20\,\curvearrowright}$ ${10},$ $-10,$ $-30,$ $-50,...$ This is the explicit formula for the arithmetic sequence $10,-10,-30,-50,...$. $c(n)={10}{-20}(n-1)$ Note that this solution strategy results in this formula, however an equally correct solution can be written in other equivalent forms as well.